Alternating Deep Low Rank Approach for Exponential Function Reconstruction and Its Biomedical Magnetic Resonance Applications

Exponential function is a fundamental signal form in general signal processing and biomedical applications, such as magnetic resonance spectroscopy and imaging. How to reduce the sampling time of these signals is an important problem. Sub-Nyquist sampling can accelerate signal acquisition but bring in artifacts. Recently, the low rankness of these exponentials has been applied to implicitly constrain the deep learning network through the unrolling of low rank Hankel factorization algorithm. However, only depending on the implicit low rank constraint cannot provide the robust reconstruction, such as sampling rate mismatches. In this work, by introducing the explicit low rank prior to constrain the deep learning, we propose an Alternating Deep Low Rank approach (ADLR) that utilizes deep learning and optimization solvers alternately. The former solver accelerates the reconstruction while the latter one corrects the reconstruction error from the mismatch. The experiments on both general exponential functions and realistic biomedical magnetic resonance data show that, compared with the state-of-the-art methods, ADLR can achieve much lower reconstruction error and effectively alleviates the decrease of reconstruction quality with sampling rate mismatches.Comment: 14 page

CloudBrain-NMR: An Intelligent Cloud Computing Platform for NMR Spectroscopy Processing, Reconstruction and Analysis

Nuclear Magnetic Resonance (NMR) spectroscopy has served as a powerful analytical tool for studying molecular structure and dynamics in chemistry and biology. However, the processing of raw data acquired from NMR spectrometers and subsequent quantitative analysis involves various specialized tools, which necessitates comprehensive knowledge in programming and NMR. Particularly, the emerging deep learning tools is hard to be widely used in NMR due to the sophisticated setup of computation. Thus, NMR processing is not an easy task for chemist and biologists. In this work, we present CloudBrain-NMR, an intelligent online cloud computing platform designed for NMR data reading, processing, reconstruction, and quantitative analysis. The platform is conveniently accessed through a web browser, eliminating the need for any program installation on the user side. CloudBrain-NMR uses parallel computing with graphics processing units and central processing units, resulting in significantly shortened computation time. Furthermore, it incorporates state-of-the-art deep learning-based algorithms offering comprehensive functionalities that allow users to complete the entire processing procedure without relying on additional software. This platform has empowered NMR applications with advanced artificial intelligence processing. CloudBrain-NMR is openly accessible for free usage at https://csrc.xmu.edu.cn/CloudBrain.htmlComment: 11 pages, 13 figure

Statistical characterization of residual noise in the low-rank approximation filter framework, general theory and application to hyperpolarized tracer spectroscopy

The use of low-rank approximation filters in the field of NMR is increasing due to their flexibility and effectiveness. Despite their ability to reduce the Mean Square Error between the processed signal and the true signal is well known, the statistical distribution of the residual noise is still undescribed. In this article, we show that low-rank approximation filters are equivalent to linear filters, and we calculate the mean and the covariance matrix of the processed data. We also show how to use this knowledge to build a maximum likelihood estimator, and we test the estimator's performance with a Montecarlo simulation of a 13C pyruvate metabolic tracer. While the article focuses on NMR spectroscopy experiment with hyperpolarized tracer, we also show that the results can be applied to tensorial data (e.g. using HOSVD) or 1D data (e.g. Cadzow filter).Comment: 26 pages, 7 figure

Noise-reduction techniques for 1H-FID-MRSI at 14.1T: Monte-Carlo validation & in vivo application

Proton magnetic resonance spectroscopic imaging (1H-MRSI) is a powerful tool that enables the multidimensional non-invasive mapping of the neurochemical profile at high-resolution over the entire brain. The constant demand for higher spatial resolution in 1H-MRSI led to increased interest in post-processing-based denoising methods aimed at reducing noise variance. The aim of the present study was to implement two noise-reduction techniques, the Marchenko-Pastur principal component analysis (MP-PCA) based denoising and the low-rank total generalized variation (LR-TGV) reconstruction, and to test their potential and impact on preclinical 14.1T fast in vivo 1H-FID-MRSI datasets. Since there is no known ground truth for in vivo metabolite maps, additional evaluations of the performance of both noise-reduction strategies were conducted using Monte-Carlo simulations. Results showed that both denoising techniques increased the apparent signal-to-noise ratio SNR while preserving noise properties in each spectrum for both in vivo and Monte-Carlo datasets. Relative metabolite concentrations were not significantly altered by either methods and brain regional differences were preserved in both synthetic and in vivo datasets. Increased precision of metabolite estimates was observed for the two methods, with inconsistencies noted on lower concentrated metabolites. Our study provided a framework on how to evaluate the performance of MP-PCA and LR-TGV methods for preclinical 1H-FID MRSI data at 14.1T. While gains in apparent SNR and precision were observed, concentration estimations ought to be treated with care especially for low-concentrated metabolites.Comment: Brayan Alves and Dunja Simicic are joint first authors. Currently in revision for NMR in Biomedicin

Real-Space Inversion and Super-Resolution of Ultrafast Scattering using Natural Scattering Kernels

Directly resolving in real-space multiple atomic motions using ultrafast x-ray or electron scattering is generally limited by the finite detector range. As a result, signal interpretation mostly relies on modeling and simulations of specific excitation pathways. Here, we introduce an approach to resolve ultrafast diffuse scattering signals in real space below the diffraction limit, and recover multiple atomic motions de-novo, using a scattering basis representation that is composed of the measurement parameters and constraints, and the subsequent inversion analysis. We leverage signal priors, such as smoothness and sparsity to deconvolve the spatially transformed signals using convex optimization. We validate the approach on simulated and experimental data, demonstrate super-resolution in real space, and discuss the recovery accuracy and resolution limits vs signal fidelity.Comment: 6 pages, 4 figure

Optimizing Magnetic Resonance Imaging for Image-Guided Radiotherapy

Magnetic resonance imaging (MRI) is playing an increasingly important role in image-guided radiotherapy. MRI provides excellent soft tissue contrast, and is flexible in characterizing various tissue properties including relaxation, diffusion and perfusion. This thesis aims at developing new image analysis and reconstruction algorithms to optimize MRI in support of treatment planning, target delineation and treatment response assessment for radiotherapy. First, unlike Computed Tomography (CT) images, MRI cannot provide electron density information necessary for radiation dose calculation. To address this, we developed a synthetic CT generation algorithm that generates pseudo CT images from MRI, based on tissue classification results on MRI for female pelvic patients. To improve tissue classification accuracy, we learnt a pelvic bone shape model from a training dataset, and integrated the shape model into an intensity-based fuzzy c-menas classification scheme. The shape-regularized tissue classification algorithm is capable of differentiating tissues that have significant overlap in MRI intensity distributions. Treatment planning dose calculations using synthetic CT image volumes generated from the tissue classification results show acceptably small variations as compared to CT volumes. As MRI artifacts, such as B1 filed inhomogeneity (bias field) may negatively impact the tissue classification accuracy, we also developed an algorithm that integrates the correction of bias field into the tissue classification scheme. We modified the fuzzy c-means classification by modeling the image intensity as the true intensity corrupted by the multiplicative bias field. A regularization term further ensures the smoothness of the bias field. We solved the optimization problem using a linearized alternating direction method of multipliers (ADMM) method, which is more computational efficient over existing methods. The second part of this thesis looks at a special MR imaging technique, diffusion-weighted MRI (DWI). By acquiring a series of DWI images with a wide range of b-values, high order diffusion analysis can be performed using the DWI image series and new biomarkers for tumor grading, delineation and treatment response evaluation may be extracted. However, DWI suffers from low signal-to-noise ratio at high b-values, and the multi-b-value acquisition makes the total scan time impractical for clinical use. In this thesis, we proposed an accelerated DWI scheme, that sparsely samples k-space and reconstructs images using a model-based algorithm. Specifically, we built a 3D block-Hankel tensor from k-space samples, and modeled both local and global correlations of the high dimensional k-space data as a low-rank property of the tensor. We also added a phase constraint to account for large phase variations across different b-values, and to allow reconstruction from partial Fourier acquisition, which further accelerates the image acquisition. We proposed an ADMM algorithm to solve the constrained image reconstruction problem. Image reconstructions using both simulated and patient data show improved signal-to-noise ratio. As compared to clinically used parallel imaging scheme which achieves a 4-fold acceleration, our method achieves an 8-fold acceleration. Reconstructed images show reduced reconstruction errors as proved on simulated data and similar diffusion parameter mapping results on patient data.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143919/1/llliu_1.pd

Application of the adjoint modal formalism for the design of nanooptical structures

Die vorliegende Arbeit behandelt die Analyse und das Design funktionaler nanooptischer Strukturen mit Hilfe modaler mathematischer Methoden. Diese basieren auf dem Reziprozitätstheorem der Elektrodynamik und erlauben es, den machtvollen mathematischen Apparat der Funktionalanalysis und Operatorenalgebra analog zur Quantenmechanik zu benutzen. Bei Vorliegen von dissipativen Verlusten, wie sie in der Plasmonik üblich sind, muss zu einer nicht-hermiteschen Operatorenalgebra auf Basis adjungierter, biorthogonaler Moden übergegangen werden. Diese stehen hierbei physikalisch im Zusammenhang mit den rückwärts propagierenden Moden eines optischen Systems. Nach der Darstellung des mathematischen Formalismus wird dieser auf verschiedene Probleme der Konzeption nanooptischer Systeme angewandt. Zunächst wird ein allgemeiner Ausdruck für das Impedanzverhältnis zweier beliebiger photonischer Systeme abgeleitet. Dies wird für verschiedene in der Plasmonik relevante Fälle spezialisiert. Es wird gezeigt, dass die Ausdrücke die natürliche Verallgemeinerung der bekannten Formeln aus dem Feld der Elektronik darstellen. Das modale Framework wird weiterhin eingesetzt, um die Resonanz einer Nanoantenne durch Beeinflussung der modalen Koppelmechanismen zu verstärken. Dieser Ansatz wird mittels nichtlinearer Photoelektronen-Emissions-Mikroskopie experimentell überprüft. Das letzte Kapitel widmet sich der Untersuchung von über einen dielektrischen Wellenleiter gekoppelten plasmonischen Nanopartikeln. Es wird gezeigt, dass der Kopplungsmechanismus sich zur gezielten Beeinflussung der hybriden Blochmoden-Dispersion einsetzen lässt und es so möglich wird, extreme Lichtzustände mit z.B. unendlicher oder negativer Gruppengeschwindigkeit experimentell zu realisieren und auf der theoretischen Ebene zu verstehen

Ultrasound shear wave imaging for diagnosis of nonalcoholic fatty liver disease

Pour le diagnostic et la stratification de la fibrose hépatique, la rigidité du foie est un biomarqueur quantitatif estimé par des méthodes d'élastographie. L'élastographie par ondes de cisaillement (« shear wave », SW) utilise des ultrasons médicaux non invasifs pour évaluer les propriétés mécaniques du foie sur la base des propriétés de propagation des ondes de cisaillement. La vitesse des ondes de cisaillement (« shear wave speed », SWS) et l'atténuation des ondes de cisaillement (« shear wave attenuation », SWA) peuvent fournir une estimation de la viscoélasticité des tissus. Les tissus biologiques sont intrinsèquement viscoélastiques et un modèle mathématique complexe est généralement nécessaire pour calculer la viscoélasticité en imagerie SW. Le calcul précis de l'atténuation est essentiel, en particulier pour une estimation précise du module de perte et de la viscosité. Des études récentes ont tenté d'augmenter la précision de l'estimation du SWA, mais elles présentent encore certaines limites. Comme premier objectif de cette thèse, une méthode de décalage de fréquence revisitée a été développée pour améliorer les estimations fournies par la méthode originale de décalage en fréquence [Bernard et al 2017]. Dans la nouvelle méthode, l'hypothèse d'un paramètre de forme décrivant les caractéristiques spectrales des ondes de cisaillement, et assumé initialement constant pour tous les emplacements latéraux, a été abandonnée permettant un meilleur ajustement de la fonction gamma du spectre d'amplitude. En second lieu, un algorithme de consensus d'échantillons aléatoires adaptatifs (« adaptive random sample consensus », A-RANSAC) a été mis en œuvre pour estimer la pente du paramètre de taux variable de la distribution gamma afin d’améliorer la précision de la méthode. Pour valider ces changements algorithmiques, la méthode proposée a été comparée à trois méthodes récentes permettant d’estimer également l’atténuation des ondes de cisaillements (méthodes de décalage en fréquence, de décalage en fréquence en deux points et une méthode ayant comme acronyme anglophone AMUSE) à l'aide de données de simulations ou fantômes numériques. Également, des fantômes de gels homogènes in vitro et des données in vivo acquises sur le foie de canards ont été traités. Comme deuxième objectif, cette thèse porte également sur le diagnostic précoce de la stéatose hépatique non alcoolique (NAFLD) qui est nécessaire pour prévenir sa progression et réduire la mortalité globale. À cet effet, la méthode de décalage en fréquence revisitée a été testée sur des foies humains in vivo. La performance diagnostique de la nouvelle méthode a été étudiée sur des foies humains sains et atteints de la maladie du foie gras non alcoolique. Pour minimiser les sources de variabilité, une méthode d'analyse automatisée faisant la moyenne des mesures prises sous plusieurs angles a été mise au point. Les résultats de cette méthode ont été comparés à la fraction de graisse à densité de protons obtenue de l'imagerie par résonance magnétique (« magnetic resonance imaging proton density fat fraction », MRI-PDFF) et à la biopsie du foie. En outre, l’imagerie SWA a été utilisée pour classer la stéatose et des seuils de décision ont été établis pour la dichotomisation des différents grades de stéatose. Finalement, le dernier objectif de la thèse consiste en une étude de reproductibilité de six paramètres basés sur la technologie SW (vitesse, atténuation, dispersion, module de Young, viscosité et module de cisaillement). Cette étude a été réalisée chez des volontaires sains et des patients atteints de NAFLD à partir de données acquises lors de deux visites distinctes. En conclusion, une méthode robuste de calcul du SWA du foie a été développée et validée pour fournir une méthode de diagnostic de la NAFLD.For diagnosis and staging of liver fibrosis, liver stiffness is a quantitative biomarker estimated by elastography methods. Ultrasound shear wave (SW) elastography utilizes noninvasive medical ultrasound to assess the mechanical properties of the liver based on the monitoring of the SW propagation. SW speed (SWS) and SW attenuation (SWA) can provide an estimation of tissue viscoelasticity. Biological tissues are inherently viscoelastic in nature and a complex mathematical model is usually required to compute viscoelasticity in SW imaging. Accurate computation of attenuation is critical, especially for accurate loss modulus and viscosity estimation. Recent studies have made attempts to increase the precision of SWA estimation, but they still face some limitations. As a first objective of this thesis, a revisited frequency-shift method was developed to improve the estimates provided by the original implementation of the frequency-shift method [Bernard et al 2017]. In the new method, the assumption of a constant shape parameter of the gamma function describing the SW magnitude spectrum has been dropped for all lateral locations, allowing a better gamma fitting. Secondly, an adaptive random sample consensus algorithm (A-RANSAC) was implemented to estimate the slope of the varying rate parameter of the gamma distribution to improve the accuracy of the method. For the validation of these algorithmic changes, the proposed method was compared with three recent methods proposed to estimate SWA (frequency-shift, two-point frequency-shift and AMUSE methods) using simulation data or numerical phantoms. In addition, in vitro homogenous gel phantoms and in vivo animal (duck) liver data were processed. As a second objective, this thesis also aimed at improving the early diagnosis of nonalcoholic fatty liver disease (NAFLD), which is necessary to prevent its progression and decrease the overall mortality. For this purpose, the revisited frequency-shift method was tested on in vivo human livers. The new method's diagnosis performance was investigated with healthy and NAFLD human livers. To minimize sources of variability, an automated analysis method averaging measurements from several angles has been developed. The results of this method were compared to the magnetic resonance imaging proton density fat fraction (MRI-PDFF) and to liver biopsy. SWA imaging was used for grading steatosis and cut-off decision thresholds were established for dichotomization of different steatosis grades. As a third objective, this thesis is proposing a reproducibility study of six SW-based parameters (speed, attenuation, dispersion, Young’s modulus, viscosity and shear modulus). The assessment was performed in healthy volunteers and NAFLD patients using data acquired at two separate visits. In conclusion, a robust method for computing the liver’s SWA was developed and validated to provide a diagnostic method for NAFLD